“The median black family, with just over $3,500, owns just 2 percent of the wealth of the nearly $147,000 the median white family owns. The median Latino family, with just over $6,500, owns just 4 percent of the wealth of the median white family. Put differently, the median white family has 41 times more wealth than the median black family and 22 times more wealth than the median Latino family.”
Frequency Distributions and Percentages
Political scientists use basic and sophisticated quantitative and qualitative research methods in their work. Reviewing those methods is beyond the scope of this introductory text. Still, you should be familiar with the following basic analytical techniques.
One of the most basic operations we can do in quantitative analysis is to sort things into categories and count how many instances fit into each category. Another is to translate raw numbers into percentages. Performing these basic tasks creates a data table or histogram, like a bar chart. Let’s look at something simple—like the number of associate’s and bachelor’s degrees conferred in the United States—and sort them into male and female categories to see if anything interesting happened between 1970 and 2000. Note that adding the percentage awarded to men and women each year helps us see what happened in this time period.
Table 1: Frequency Distribution and Degrees Conferred Percentages by Level and Sex 1970-2000
Source: National Center for Education Statistics (2)
This is very helpful. Table 1 shows higher education’s growing popularity for both sexes in the United States. Associate’s degree numbers more than tripled in 30 years, while bachelor’s degree numbers nearly doubled. But the really interesting story has to do with the proportion of degrees women and men received. Can you see it? If you look carefully you can. The difficulty in seeing what is happening is a common one with frequency distributions. Because the total number of degrees in each category changes year by year, it is not always easy to see patterns in the blizzard of raw numbers. I’ve converted the raw numbers into percentages for each year and for each degree. For example, in 1970, 206,000 associate’s degrees were conferred; 89,000, or 43 percent, went to women. Now look how easy it is to see what has been happening. We can clearly see that at both the associate’s and bachelor’s level, the percentage of degrees earned by women has grown since 1970 while the percentage earned by men has slipped. Even simple quantitative analysis such as this can be very powerful and can prompt political scientists and sociologists to dig deeper. What caused this shift? What political, social, and economic impacts did this shift produce? Can we find evidence of those impacts today?
It’s easier for the brain to figure out what’s happening here if we translate the raw numbers into percentages, because doing so highlights the actual proportion of degrees received by type per year. In this course, you absolutely, positively must be able to figure percentages. An easy way to remind yourself how to do that is to remember the simple phrase, “part over total, times one hundred, equals percent.” Before we go back to the table, let’s look at a few examples. A class has 35 students; 13 are wearing sandals. We can find the percentage of students who are wearing sandals by dividing the part—13 sandal-wearing students, by the total—35 students in the class, and multiplying by 100. So, the equation is as follows:
13/35 x 100 or .37 x 100 equals 37 percent
Another example: If 10,458 of a college’s total enrollment of 18,145 students register to vote, what percentage of the student body is registered to vote? Again, we find the answer by dividing the part—10,458 students registered—by the entire student-body total, which is 18,145, and multiplying by 100. The equation is as follows:
10,458/18,145 x 100 or .58 x 100 equals 58 percent
When dealing with percentages, the part can be a larger number than the total if we are figuring percentages larger than 100 percent. Let’s go back to Table 1. For 1970, the total associate’s degrees conferred was 206,000, and the total bachelor’s degrees conferred was 792,000. The numbers of both degrees increased by the year 2000, but what if we wanted to know whether the associate’s degree numbers increased proportionally more than the bachelor’s degree numbers from 1970 to 2000? We would proceed like this: Put the 2000 associate’s degree number over the 1970 associate’s degree number and multiply by 100. Do the same thing for the bachelor’s degree numbers and compare.
Associate’s degrees: 565,000/206,000 x 100 equals 274 percent
Bachelor’s degrees: 1,238,000/792,000 x 100 equals 156 percent
We can say that while the bachelor’s degree numbers increased by 56 percent from 1970 to 2000, the associate’s degree numbers increased even more—fully 174 percent in the same time period.
Measures of Central Tendency
For many kinds of variables, we can go beyond frequency distributions and percentages and calculate simple measures of central tendency. What we are trying to do here is to describe the typical value among all those in our data sample. The two most useful measures of central tendency are the mean and median. The mean is the average of a group of numbers. The median is the middle value of a range of numbers, meaning half the data set is higher and half is lower in value.
You calculate the mean by adding up all the variables’ values and divide by the number of values in the set. In this example, the variable is salaries, and there are six values in the set. Let’s calculate a group’s mean or average salary.
||Step 1: Add up all of the salaries, which in this case is $223,100.
Step 2: Count the number of values you have, which in this case is six. There are six salaries in the data set.
Step 3: Divide $223,100 by six, resulting in a mean or average salary of $37,183.
We might also be interested in the value that falls right in the middle of our salary data distribution. This is called the median. Specifically, the median is defined as the value that has the same number of values above it as it has below it. Here’s how you would calculate the median value of the same data set.
||Step 1: Organize the data points in ascending or descending order.
Step 2: If the total number of values is an odd number, the mean is the value right in the middle. If Aidan wasn’t in our sample, Ahmed’s $37,500 salary would be the median.
Step 3: If the total number of values is an even number, as in our sample, the median is the average of the two middle numbers. Our two middle numbers are $36,000 and $37,500, and the mean or average of those two numbers is $36,750. That’s the median.
When data conform more or less to a normal distribution curve, the median and the mean are usually close together. There is one circumstance when the median and mean differ considerably, and that’s when the data are skewed to one side or the other—often by a few outlying data values. Let’s assume that a new person joins our group. She is paid considerably more than the others.
||Differences Between the Mean and the Median
Mean = $746,157—total salaries divided by 7
Median = $37,500—Ahmed’s salary, which is in the middle of the set.
When Oprah walks into the room, suddenly the mean salary jumps up to three-quarters of a million dollars, while the median only bumps up to $37,500. Which is a more accurate economic descriptor of how well these people are doing? In this case, the median is more useful than the mean.
Many researchers in a variety of disciplines use content analyses to gain insight into textual or mass media sources. Content analyses can be defined as “a systematic, replicable technique for compressing many words of text into fewer content categories based on explicit rules of coding.” (3) Content analysis often involves something as simple as counting the frequency of particular words in a text. It may entail categorizing the people quoted and the photographs used, or it may involve measuring sentence length, vocabulary, and so on.
An effective content analysis must be done carefully. The researcher must first specify the media universe that she is going to analyze, as well as the sample from that universe. She also must be very specific about the analytical rules for counting and categorizing aspects of the text or media. Then she must rigorously follow those rules so there is no ambiguity about the findings. This last part has become much easier with the advent of computer programs that can do much of the work, sparing the researcher many hours and strained eyes.
Content analyses can yield very informative results. What if we examined all the presidential State of the Union speeches and looked for religious references? Would the frequency of those references change over time? Would they be related to the policies pursued by each administration? What if we examined all local television news programs for a given time period and analyzed all references to our state’s congressional delegation? Are the references in a positive, negative, or neutral light? Do they fluctuate over the election cycle? What if we did a content analysis of two different news sites’ editorials and looked for ideological differences between them?
Surveying individuals has been a very popular analytical form in political science, sociology, marketing, psychology, and communications studies. If you want to know about people or about their opinions and knowledge, often the best thing to do is to ask them. Surveys can take several forms—from telephone interviews to in-person interviews, from controlled-environment questionnaires to mail-in questionnaires. Sometimes, a researcher wants to survey a discrete group of people—say, former Secretaries of State—in which case he will contact all the group’s members and ask them questions relevant to the research project. In other instances, the researcher is interested in surveying a large population. Because it is not feasible to survey large populations, the researcher instead selects a random sample out of the larger population and gives them the survey. Using statistical techniques, the researcher can state with much confidence that the answers given by the random sample are representative of the entire population.
Survey research is a complicated field that we can’t do justice to here, but you should be aware of the major types of questions found in surveys.
Dichotomous Questions. These questions have only two possible answers. Questions that require a yes or no answer are dichotomous, as are questions that ask you to put yourself into one of two categories, like whether you are or are not a citizen.
Multiple-Choice Questions. These questions offer three or more defined choices from which the respondent can choose. Such a question might ask for the respondent’s ethnicity, for example, or for them to choose their favorite from a list of presidential candidates. A common type of multiple-choice question is to probe the respondent’s opinion using a Likert response scale.
Likert-Response Scale. For these questions, the respondent is probed for his or her agreement level with a statement. For example: “The death penalty is justifiable in some circumstances—strongly disagree; disagree; neutral; agree; strongly agree.”
Thermometer-Scale Questions. Very often these are called “feeling thermometers” because they are usually used to probe the respondent’s affect toward a certain subject or person. In an in-person setting, the respondent is presented with a thermometer that runs from 0 to 100 and is asked to point at the thermometer to reflect their positive or negative feeling. For example, we might show photos of political candidates to the subjects, who would then point to 89 for one candidate, 14 for another candidate, 67 for a third candidate, and so forth.
Ranking-List Questions. These questions present the respondent with a list of items and asks him or her to rate the item’s importance. For example, we might do this with a list of issues facing the country. The respondent gives the most important issue a 1, the second most important issue a 2, and so on.
Open-Ended Questions. These questions provide the respondent with much freedom to structure the answer for themselves. Instead of ranking issues facing the country, the survey might simply ask the person: “What do you think is the most important issue facing the United States?” Or, the researcher can follow a multiple-choice question about which candidate the respondent supports with an open-ended question, such as, “Why do you support that candidate?”
Survey research results are heavily dependent on question wording. When you see public opinion polls cited in the media, and the question’s exact wording is not published, you should be suspicious and look for the original survey so that you can check the wording. How questions are worded can have major impacts on major issues like, how much government spending people support. For example, consider the following two versions of a question:
- Are we spending too much, too little, or about the right amount on welfare?
- Are we spending too much, too little, or about the right amount on assistance to the poor?
One study found that the public was about 41 percentage points more likely to support more “assistance to the poor” than it was to support “welfare.” (4)
The other thing to look for is whether the poll is a legitimate attempt to gauge the public’s opinion or if it’s a push poll. A push poll combines a survey with biased information designed to get the results the sponsoring organization or candidate is looking for. Push polls have been denounced by all legitimate survey research organizations. (5) In a push poll, the pollster tells subjects things like (made-up example) “Representative Jones wants to give tax breaks to yacht owners and wants to end all women’s bodily autonomy,” and then the pollster poses a question like, “Should representative Jones be re-elected?” When the mostly negative results come back, the sponsoring organization or opposing candidate will try to feed the media information about Representative Jones being unpopular with his constituents.
A smart beginning to conducting any political analysis is to organize information into a typology. A typology is a visual device that allows you to systematically classify types that have common characteristics. All sorts of political events, things, and people can be sorted in a typology. Use a basic typology to sort things by how they score on two important dimensions. Over two thousand years ago, Aristotle created a typology of different types of governing systems. Aristotle’s two dimensions were who ruled and in whose interest they ruled, producing a typology that looks like this:
The first thing to notice is that terminology has changed since Aristotle’s time. He equated democracy with mob rule—the masses ruling in their own selfish and short-sighted interest. He also makes a different distinction than we do between aristocracy and oligarchy as though the main difference was in whose interest the few ruled. Today, we tend to see aristocracies as ruling in their selfish interest just like we do oligarchies. The main takeaway is that Aristotle thoughtfully tried to apply what he knew about political regimes in a systematic way. You can do the same thing with presidential vetoes, elections, congressional bills, political demonstrations, or just about any political phenomenon in which you have enough cases to categorize. One important rule of typologies is that the interior cells must be mutually exclusive—that is, the things that you are categorizing must fit in one—and only one—box. A political system cannot be both a polity and a monarchy in Aristotle’s typology.
- National Center for Education Statistics
- Steve Stemler, “An Introduction to Content Analysis,” ERIC. June 2001.
- Kenneth A. Rasinski, “The Effect of Question Wording on Public Support for Government Spending,” Public Opinion Quarterly. 53(3): Autumn, 1989. Pages 388-394.
- Marjorie Connelly, “Push Polls, Defined,” The New York Times. June 18, 2014.
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